1. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 1 Theory summary: what I would like to understand Jiří Chýla, Institute of Physics, Prague Overview on direct photons: Heinrich Total cross sections: Pancheri, GPD’s & related: Friot, Landsberg, Pire, Wallon, Szymanowski Unintegrated PDF: Szczurek, Hautman Standard PDF: JC, Hejbal, Sasaki Power corrections: Hautman Scales, schemes: Geiser, Grindhammer QED processes: Serbo, Da Silva Often difficult to distinguish between theory/phenome- and experiment. A lot of comparison of older calcula- tions with new data, as well as new calculations.

2. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 2 I will not attempt to summarize what the speakers actually said, but will attach to each of the topics comments/questions, the latter mostly reflecting my ignorance of the respective subjects, but which, nevertheless, might be interesting to answer.

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4. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 4 What about dijets?

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6. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 6 significant achievement!

7. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 7 G. Pancheri: Total cross sections

8. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 8 What drives the rise of the total cross sections? G. Pancheri has the answer: minijet production driven by the rise of PDF at low x

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10. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 10 To get the rise she needs very small lower cut off on minijet, or better, produced parton, tranverse momentum But as such low transverse momenta:  lowest order partonic cross sections are unreliable and highly ambiguous (scales!).  These XS grow rapidly at low p T and thus the rise of the total XS is very sensitive to the choice of p T min  I do not understand how one can use in minijet models PDF extracted from genuine hard processes.

11. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 11 Generalized PDF and similar quantities From Wallon’s talk: Factorization on the level of partonic cross sections Factorization on the level of partonic amplitudes

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14. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 14 Great, but factorization implies ambiguities, scales and schemes, which at least for inclusive processes, play very important phenomenological role. I would expect them to play analogous role in GPD’s and related quantities as well. Is that true? If yes, there must a mechanism to guarantee independence of physical quantities of these ambiguities, similarly as in inclusive processes: Choice of C (1) here is compensated by change of C (1) here Mechanism guaranteeing factorization scale and scheme invariance of proton structure function compensation

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16. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 16 DA: TDA:

17. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 17 Looks like the LO purely perturbative quantity contain information on the structure of hadrons No unknown nonperturbative input needed ? No factorization scale introduced ? How to choose ? ?+?+

18. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 18 Unintegrated PDF Used by Szczurek to describe data on inclusive direct photon production in hadronic collisions meaning of this scale?

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20. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 20 but where is ?

21. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 21 I miss the mechanism by which the dependence of UPDF’s on the scale is cancelled. In the standard integrated PDF’s this cancellation is provided is by the explicit depen- dence of hard scattering cross sections on. So the off-shell cross sections should depend on it as well, and one would probably need NLO QCD calculation of these cross sections to get the cancellation mechanism. At the present time the scale dependence of calculations involving UPDF’s is therefore large. But perhaps, I am wrong....

22. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 22 Standard, integrated PDF and structure of the photon Real photon: alternative organization of finite order QCD approximations to photon structure function Basic message: parton distribution functions of the photon do not behave like Together with the plea above this implies significantly different definitions of LO and NLO approximations to Plea: apply the terms “LO”, “NLO” etc to QCD contribu- tions only as well as other photon induced processes.

23. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 23 Numerical differences between standard and alternative approaches and their phenomenological relevance shown by J. Hejbal:

24. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 24 Virtual photon: new NNLO (in the standard definition) calculations of the “Order” defined in terms of high Q 2 behavior of the structure function, as understood in the pioneering papers of Witten, De Witt et al. and Llewelyn-Smith.

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26. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 26 apart from the last term behaves as for

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28. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 28 Scales, schemes Boring, frustrating but inevitable perturbation theory ambiguities. We can ignore them, but to our own peril. Achim Geiser: How well do we understand choice of QCD scales? These ambiguities are inevitable consequence of renor- malization and factorization procedures and truncation of PT to any fixed order. Contrary to conventional view, they do not go away when we go to higher orders, as at each order of PT new free parameters defining renormalized/factorized quantities do appear. There is no genuine “resolution” of these ambiguities, just a few recipes how to fix the scales and schemes.

29. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 29 Achim Geiser’s

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31. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 31 Achim Geiser’s

32. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 32 I generally agree with Achim’s strategy, but want to emphasize two points:  Renormalization schemes are equally important as renormalization scales. We can fix one and very the other or the other way round. The number “1/2” in Achim’s suggested new default scale corresponds to the standard MS bar RS. In other RS it will be different and could easily be 1.  The renormalization and factorization scales should not be identified (as usually done). Reply to Samuel Wallon: BLM scale setting method cannot be applied to quantities involving factorization scale.

33. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 33 NLO calculation of bbbar production at the Tevatron Example of different renormalization and factorization scale dependence:

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39. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 39 Power corrections and low x physics

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41. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 41 But: separation of perturbative part and power corrections is ambiguous and the numerical relevance of the latter thus depends on the choice of free parameters (scales, schemes) of perturbative calculations. Example: Klaus Hammacher at ICHEP 2002 in Amsterdam

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47. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 47 QED processes are not boring V. Serbo: Large contribution of the Delbruck scattering into process of a photon emission in collisions of relatis- tic nuclei.

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49. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 49 Da Silva: Four fermion two pair production from gamma- gamma collisions: from PLC to LHC Motivation - Need for a reference process for luminosity measurement at a PLC - QED and QCD back- ground source to rare processes - Only a realistic Monte- Carlo can give a correct result But these processes are of great interest for heavy quark production in collisions!

50. Jiri ChylaPhoton 2007, Paris, July 9-13, 2007 50 Au revoir in 2009 at DESY